Constructing Hopf braces

We investigate Hopf braces, a concept recently introduced by Angiono, Galindo and Vendramin [I. Angiono, C. Galindo and L. Vendramin, Hopf braces and Yang-Baxter operators, Proc. Amer. Math. Soc. 145 (2017) 1981-1995] in connection to the quantum Yang-Baxter equation. More precisely, we propose two methods for constructing Hopf braces. The first one uses matched pairs of Hopf algebras while the second one relies on category-theoretic tools.